scholarly journals Schur multipliers of special 𝑝-groups of rank 2

2020 ◽  
Vol 23 (1) ◽  
pp. 85-95
Author(s):  
Sumana Hatui
Keyword(s):  
Prime Power ◽  
Prime Power Order ◽  
Schur Multiplier ◽  
Schur Multipliers ◽  
Rank 2

AbstractLet G be a special p-group with center of order {p^{2}}. Berkovich and Janko asked to find the Schur multiplier of G in [Y. Berkovich and Z. Janko, Groups of Prime Power Order. Volume 3, De Gruyter Exp. Math. 56, Walter de Gruyter, Berlin, 2011; Problem 2027]. In this article, we answer this question by explicitly computing the Schur multiplier of these groups.

The Homological Functors of Some Abelian Groups of Prime Power Order

2014 ◽  
Vol 71 (5) ◽  
Author(s):  
Rosita Zainal ◽  
Nor Muhainiah Mohd Ali ◽  
Nor Haniza Sarmin ◽  
Samad Rashid
Keyword(s):  
Tensor Product ◽  
Prime Power ◽  
Homotopy Theory ◽  
Abelian Groups ◽  
Prime Power Order ◽  
Schur Multiplier ◽  
Integer Coefficients ◽  
Nonabelian Tensor ◽  
Tensor Square ◽  
Special Case

The homological functors of a group were first introduced in homotopy theory. Some of the homological functors including the nonabelian tensor square and the Schur multiplier of abelian groups of prime power order are determined in this paper. The nonabelian tensor square of a group G introduced by Brown and Loday in 1987 is a special case of the nonabelian tensor product. Meanwhile, the Schur multiplier of G is the second cohomology with integer coefficients is named after Issai Schur. The aims of this paper are to determine the nonabelian tensor square and the Schur multiplier of abelian groups of order p5, where p is an odd prime

Finite p-groups all of whose maximal subgroups, except one, have cyclic derived subgroups

2014 ◽  
Vol 14 (01) ◽  
pp. 1450080
Author(s):  
Zvonimir Janko
Keyword(s):  
Maximal Subgroup ◽  
Prime Power ◽  
Maximal Subgroups ◽  
Prime Power Order ◽  
Derived Subgroup ◽  
Rank 2

Let G be a finite p-group which has exactly one maximal subgroup H such that its derived subgroup H' is noncyclic. Then we must have p = 2, G′ is abelian of rank 2, |G′ : H′| = 2 and d (G) = 2 or 3 (Theorems 6 and 8). This solves the problem No. 2248 stated by Berkovich in [Groups of Prime Power Order, Vol. 3 (Walter de Gruyter, Berlin, 2011)].

scholarly journals A bound on the Schur multiplier of a prime-power group

1999 ◽  
Vol 60 (2) ◽  
pp. 191-196 ◽  
Author(s):  
Graham Ellis ◽  
James Wiegold
Keyword(s):  
Upper Bound ◽  
Prime Power ◽  
Schur Multiplier ◽  
Schur Multipliers ◽  
Power Group

The paper improves on an upper bound for the order of the Schur multiplier of a finite p-group given by Wiegold in 1969. The new bound is applied to the problem of classifying p-groups according to the size of their Schur multipliers.

scholarly journals The energy of integral circulant graphs with prime power order

2011 ◽  
Vol 5 (1) ◽  
pp. 22-36 ◽  
Author(s):  
J.W. Sander ◽  
T. Sander
Keyword(s):  
Adjacency Matrix ◽  
Prime Power ◽  
Prime Power Order ◽  
Circulant Graph ◽  
Closed Formula ◽  
Circulant Graphs ◽  
Vertex Set

The energy of a graph is the sum of the moduli of the eigenvalues of its adjacency matrix. We study the energy of integral circulant graphs, also called gcd graphs. Such a graph can be characterized by its vertex count n and a set D of divisors of n such that its vertex set is Zn and its edge set is {{a,b} : a, b ? Zn; gcd(a-b, n)? D}. For an integral circulant graph on ps vertices, where p is a prime, we derive a closed formula for its energy in terms of n and D. Moreover, we study minimal and maximal energies for fixed ps and varying divisor sets D.

Space groups and groups of prime-power order II

1980 ◽  
Vol 35 (1) ◽  
pp. 203-209 ◽  
Author(s):  
H. Finken ◽  
J. Neub�ser ◽  
W. Plesken
Keyword(s):  
Prime Power ◽  
Prime Power Order ◽  
Space Groups

On S-Quasinormal and C-Normal Subgroups of Prime Power Order in Finite Groups

2011 ◽  
Vol 18 (04) ◽  
pp. 685-692
Author(s):  
Xuanli He ◽  
Shirong Li ◽  
Xiaochun Liu
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Prime Power ◽  
Maximal Subgroups ◽  
Prime Power Order ◽  
Normal Subgroups ◽  
A Finite Group

Let G be a finite group, p the smallest prime dividing the order of G, and P a Sylow p-subgroup of G with the smallest generator number d. Consider a set [Formula: see text] of maximal subgroups of P such that [Formula: see text]. It is shown that if every member [Formula: see text] of is either S-quasinormally embedded or C-normal in G, then G is p-nilpotent. As its applications, some further results are obtained.

scholarly journals Automorphism orbits of finite groups

1986 ◽  
Vol 40 (2) ◽  
pp. 253-260 ◽  
Author(s):  
Thomas J. Laffey ◽  
Desmond MacHale
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Finite Groups ◽  
Prime Power ◽  
Structure Theorem ◽  
Equivalence Classes ◽  
Prime Power Order ◽  
A Finite Group

AbstractLet G be a finite group and let Aut(G) be its automorphism group. Then G is called a k-orbit group if G has k orbits (equivalence classes) under the action of Aut(G). (For g, hG, we have g ~ h if ga = h for some Aut(G).) It is shown that if G is a k-orbit group, then kGp + 1, where p is the least prime dividing the order of G. The 3-orbit groups which are not of prime-power order are classified. It is shown that A5 is the only insoluble 4-orbit group, and a structure theorem is proved about soluble 4-orbit groups.

scholarly journals On c-normality of finite groups

2005 ◽  
Vol 78 (3) ◽  
pp. 297-304 ◽  
Author(s):  
M. Asaad ◽  
M. Ezzat Mohamed
Keyword(s):  
Normal Subgroup ◽  
Finite Groups ◽  
Prime Power ◽  
Prime Power Order

AbstractA subgroup H of a finite G is said to be c-normal in G if there exists a normal subgroup N of G such that G = HN with H ∩ N ≤ HG = CoreG(H). We are interested in studying the influence of the c–normality of certain subgroups of prime power order on the structure of finite groups.

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